Harmonic Analysis On Free Groups
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Harmonic Analysis On Free Groups
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Author : Alessandro Figa-Talamanca
language : en
Publisher: CRC Press
Release Date : 2020-11-26
Harmonic Analysis On Free Groups written by Alessandro Figa-Talamanca and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-26 with Mathematics categories.
This book presents an account of recent results on the theory of representations and the harmonic analysis of free groups. It emphasizes the analogy with the theory of representations of noncompact semisimple Lie groups and restricts the focus to a class of irreducible unitary representations.
Harmonic Analysis On Free Groups
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Author : Figa-Talamanca
language : en
Publisher: CRC Press
Release Date : 2017-06-30
Harmonic Analysis On Free Groups written by Figa-Talamanca and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-30 with categories.
Harmonic Analysis On Classical Groups
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Author : Gong Sheng
language : en
Publisher: Springer
Release Date : 1991
Harmonic Analysis On Classical Groups written by Gong Sheng and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Group theory categories.
I. Harmonic Analysis on Unitary Groups.- 0. Preliminary.- 1. Abel Summation of Fourier Series on Unitary Groups.- 2. Cesàro Summations of Fourier Series on Unitary Groups.- 3. Partial Sum of Fourier Series on Unitary Groups.- 4. On Peter-Weyl Theorem.- 5. Spherical Summation of Fourier Series on Unitary Groups.- II. Harmonic Analysis on Rotation Groups.- 6. Abel Summation of Fourier Series on Rotation Groups.- 7. Cesàro Summation of Fourier Series on Rotation Groups.- 8. Partial Sum of Fourier Series on Rotation Groups.- 9. Spherical Summation of Fourier Series on Rotation Groups.- III. Harmonic Analysis on Unitary Symplectic Groups.- 10. The Volume of Unitary Symplectic Group and Criteria of Convergence of Fourier Series.- 11. Cesàro and Abel Summation of Fourier Series on Unitary Symplectic Groups.- 12. Spherical Summation of Fourier Series on Unitary Symplectic Groups.- 13. Harmonic Analysis in Classical Domains on Quaternion Field.- Epilogue.- References.
Harmonic Analysis Of Spherical Functions On Real Reductive Groups
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Author : Ramesh Gangolli
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Harmonic Analysis Of Spherical Functions On Real Reductive Groups written by Ramesh Gangolli and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Analysis on Symmetric spaces, or more generally, on homogeneous spaces of semisimple Lie groups, is a subject that has undergone a vigorous development in recent years, and has become a central part of contemporary mathematics. This is only to be expected, since homogeneous spaces and group representations arise naturally in diverse contexts ranging from Number theory and Geometry to Particle Physics and Polymer Chemistry. Its explosive growth sometimes makes it difficult to realize that it is actually relatively young as mathematical theories go. The early ideas in the subject (as is the case with many others) go back to Elie Cart an and Hermann Weyl who studied the compact symmetric spaces in the 1930's. However its full development did not begin until the 1950's when Gel'fand and Harish Chandra dared to dream of a theory of representations that included all semisimple Lie groups. Harish-Chandra's theory of spherical functions was essentially complete in the late 1950's, and was to prove to be the forerunner of his monumental work on harmonic analysis on reductive groups that has inspired a whole generation of mathematicians. It is the harmonic analysis of spherical functions on symmetric spaces, that is at the focus of this book. The fundamental questions of harmonic analysis on symmetric spaces involve an interplay of the geometric, analytical, and algebraic aspects of these spaces. They have therefore attracted a great deal of attention, and there have been many excellent expositions of the themes that are characteristic of this subject.
Harmonic Analysis On Real Reductive Groups
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Author : V.S. Varadarajan
language : en
Publisher: Springer
Release Date : 2006-11-14
Harmonic Analysis On Real Reductive Groups written by V.S. Varadarajan and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
Harmonic Analysis And Representation Theory For Groups Acting On Homogenous Trees
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Author : Alessandro Figá-Talamanca
language : en
Publisher: Cambridge University Press
Release Date : 1991-06-28
Harmonic Analysis And Representation Theory For Groups Acting On Homogenous Trees written by Alessandro Figá-Talamanca and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-06-28 with Mathematics categories.
These notes treat in full detail the theory of representations of the group of automorphisms of a homogeneous tree. The unitary irreducible representations are classified in three types: a continuous series of spherical representations; two special representations; and a countable series of cuspidal representations as defined by G.I. Ol'shiankii. Several notable subgroups of the full automorphism group are also considered. The theory of spherical functions as eigenvalues of a Laplace (or Hecke) operator on the tree is used to introduce spherical representations and their restrictions to discrete subgroups. This will be an excellent companion for all researchers into harmonic analysis or representation theory.
Harmonic Analysis On Reductive P Adic Groups
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Author : B. Harish-Chandra
language : en
Publisher:
Release Date : 2014-01-15
Harmonic Analysis On Reductive P Adic Groups written by B. Harish-Chandra and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Harmonic Analysis On Semi Simple Lie Groups
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Author : Garth Warner
language : en
Publisher:
Release Date : 1972
Harmonic Analysis On Semi Simple Lie Groups written by Garth Warner and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with Mathematics categories.
Harmonic Analysis On The Heisenberg Group
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Author : Sundaram Thangavelu
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Harmonic Analysis On The Heisenberg Group written by Sundaram Thangavelu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The Heisenberg group plays an important role in several branches of mathematics, such as representation theory, partial differential equations, number theory, several complex variables and quantum mechanics. This monograph deals with various aspects of harmonic analysis on the Heisenberg group, which is the most commutative among the non-commutative Lie groups, and hence gives the greatest opportunity for generalizing the remarkable results of Euclidean harmonic analysis. The aim of this text is to demonstrate how the standard results of abelian harmonic analysis take shape in the non-abelian setup of the Heisenberg group. Thangavelu’s exposition is clear and well developed, and leads to several problems worthy of further consideration. Any reader who is interested in pursuing research on the Heisenberg group will find this unique and self-contained text invaluable.
Harmonic Analysis On Reductive Groups
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Author : W. Barker
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Harmonic Analysis On Reductive Groups written by W. Barker and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
A conference on Harmonic Analysis on Reductive Groups was held at Bowdoin College in Brunswick, Maine from July 31 to August 11, 1989. The stated goal of the conference was to explore recent advances in harmonic analysis on both real and p-adic groups. It was the first conference since the AMS Summer Sym posium on Harmonic Analysis on Homogeneous Spaces, held at Williamstown, Massachusetts in 1972, to cover local harmonic analysis on reductive groups in such detail and to such an extent. While the Williamstown conference was longer (three weeks) and somewhat broader (nilpotent groups, solvable groups, as well as semisimple and reductive groups), the structure and timeliness of the two meetings was remarkably similar. The program of the Bowdoin Conference consisted of two parts. First, there were six major lecture series, each consisting of several talks addressing those topics in harmonic analysis on real and p-adic groups which were the focus of intensive research during the previous decade. These lectures began at an introductory level and advanced to the current state of research. Sec ond, there was a series of single lectures in which the speakers presented an overview of their latest research.